The equilibrium constant for the reaction 2SO2 + O2 <=> 2SO3(all are gases) at a certain const temperature is 846.4mol/dm^3. At equilibrium in a 1dm^3 vessel, 0.5 moles of SO2, 0.1 moles of O2, and 4.6 moles of SO3 were found. How many moles of oxygen must be added to the mixture in the vessel at the same temp to increase the amount of SO3 present at equi to 5 moles?
I tried an ICE table and everything, but I always get a really complicated cubic equation at the denominator when I try to find the rate constant. the formula I gow was (5)^2/(0.1+x)(0.5-2x)= to the rate constant. Is there something I'm doing wrong? The answer is supposed to be 3.05moles.
I didn't do the math but I don't think your set up is quite right but almost right.
K = 846.4 = (4.6-2x)^2/(0.5-2x)^2*(0.1+x)
For cubic equations you can find a calculator on the web that will solve them.
Let me point out a couple of things that I'm picky about.
1. K has no units. Your problem may show units but the thermodynamic constant has no units.
2. This is NOT a rate constant; this is an equilibrium constant. The two are not the same.
To solve this problem, you can use the principle of Le Chatelier's principle, which states that if a system at equilibrium is disturbed, the reaction will shift in the direction that counteracts the disturbance.
In this case, you want to increase the amount of SO3 present at equilibrium from 4.6 moles to 5 moles. From the balanced chemical equation - 2SO2 + O2 ⟷ 2SO3 - it can be observed that the stoichiometric ratio between SO3 and O2 is 2:1. This means that for every 2 moles of SO3 formed, 1 mole of O2 is consumed.
Let's denote the change in moles of O2 as 'x'. So, if we want to increase the amount of SO3 by 0.4 moles (from 4.6 to 5 moles), we would need to consume 0.2 moles of O2 (half of 0.4 moles). Therefore, the equation for the change in moles is:
0.2 moles of O2 = x
Now, you can calculate the total number of moles of O2 in the vessel before adding the additional O2:
Total moles of O2 = 0.1 moles of O2 + x
Plugging in the values, we have:
Total moles of O2 = 0.1 + 0.2 = 0.3 moles of O2
To determine the number of moles of O2 that need to be added, you subtract the total moles of O2 from the initial amount of O2 needed:
Moles of O2 to be added = 0.5 - 0.3 = 0.2 moles of O2
Therefore, to increase the amount of SO3 present at equilibrium to 5 moles, you need to add 0.2 moles of O2.
I hope this helps! Let me know if you have any further questions.